This thesis addresses one of the most fundamental challenges for modern science: how can the brain as a network of neurons process information, how can it create and store internal models of our world, and how can it infer conclusions from ambiguous data? The author addresses these questions with the rigorous language of mathematics and theoretical physics, an approach that requires a high degree of abstraction to transfer results of wet lab biology to formal models. The thesis starts with an in-depth description of the state-of-the-art in theoretical neuroscience, which it subsequently uses as a basis to develop several new and original ideas. Throughout the text, the author connects the form and function of neuronal networks. This is done in order to achieve functional performance of biological brains by transferring their form to synthetic electronics substrates, an approach referred to as neuromorphic computing. The obvious aspect that this transfer can never be perfect but necessarily leads to performance differences is substantiated and explored in detail. The author also introduces a novel interpretation of the firing activity of neurons. He proposes a probabilistic interpretation of this activity and shows by means of formal derivations that stochastic neurons can sample from internally stored probability distributions. This is corroborated by the author’s recent findings, which confirm that biological features like the high conductance state of networks enable this mechanism. The author goes on to show that neural sampling can be implemented on synthetic neuromorphic circuits, paving the way for future applications in machine learning and cognitive computing, for example as energy-efficient implementations of deep learning networks. The thesis offers an essential resource for newcomers to the field and an inspiration for scientists working in theoretical neuroscience and the future of computing.

Mihai Petrovici started studying Physics at the University of Heidelberg in 2001. During his early undergraduate days, he worked on particle tracking for the ALICE experiment at CERN. For his diploma thesis, he moved to solid state physics, where he studied glasses at low temperatures. He began his PhD in 2008 in the Electronic Vision(s) group of Karlheinz Meier and Johannes Schemmel, where he worked at the interface of theoretical neuroscience and neuromorphic computing, earning his doctorate with summa cum laude in 2015. During this time, he established a theoretical department within the Vision(s) group, which he is currently leading.